diff --git a/src/textual/_compositor.py b/src/textual/_compositor.py
index 74023b89c..9a623fd13 100644
--- a/src/textual/_compositor.py
+++ b/src/textual/_compositor.py
@@ -14,6 +14,7 @@ without having to render the entire screen.
 from __future__ import annotations
 
 from itertools import chain
+from collections import defaultdict
 from operator import itemgetter
 import sys
 from typing import Callable, cast, Iterator, Iterable, NamedTuple, TYPE_CHECKING
@@ -203,6 +204,8 @@ class Compositor:
         # Regions that require an update
         self._dirty_regions: set[Region] = set()
 
+        self._layers_visible: dict[int, list[tuple[Widget, Region]]] | None = None
+
     @classmethod
     def _regions_to_spans(
         cls, regions: Iterable[Region]
@@ -257,6 +260,7 @@ class Compositor:
         """
         self._cuts = None
         self._layers = None
+        self._layers_visible = None
         self.root = parent
         self.size = size
 
@@ -328,6 +332,7 @@ class Compositor:
             }
         return self._visible_widgets
 
+    @timer("arrange")
     def _arrange_root(
         self, root: Widget, size: Size
     ) -> tuple[CompositorMap, set[Widget]]:
@@ -475,6 +480,27 @@ class Compositor:
             )
         return self._layers
 
+    @property
+    def layers_visible(self) -> dict[int, list[tuple[Widget, Region]]]:
+        """Visible widgets and regions in layers order."""
+
+        if self._layers_visible is None:
+            with timer("CALC LAYERS"):
+                layers_visible: dict[int, list[tuple[Widget, Region]]]
+                screen_region = self.size.region
+                _, screen_height = self.size
+                layers_visible = {y: [] for y in screen_region.line_range}
+
+                visible_intersection = screen_region.intersection
+
+                for widget, region, *_ in self:
+                    (_x, y, _width, height) = region
+                    if y + height > 0 and y < screen_height:
+                        for y in visible_intersection(region).line_range:
+                            layers_visible[y].append((widget, region))
+                self._layers_visible = layers_visible
+        return self._layers_visible
+
     def __iter__(self) -> Iterator[tuple[Widget, Region, Region, Size, Size]]:
         """Iterate map with information regarding each widget and is position
 
@@ -514,10 +540,16 @@ class Compositor:
             tuple[Widget, Region]: A tuple of the widget and its region.
         """
         # TODO: Optimize with some line based lookup
+
         contains = Region.contains
-        for widget, cropped_region, region, *_ in self:
-            if contains(cropped_region, x, y) and widget.visible:
+        for widget, region in self.layers_visible.get(y, []):
+            if contains(region, x, y) and widget.visible:
                 return widget, region
+
+        # contains = Region.contains
+        # for widget, cropped_region, region, *_ in self:
+        #     if contains(cropped_region, x, y) and widget.visible:
+        #         return widget, region
         raise errors.NoWidget(f"No widget under screen coordinate ({x}, {y})")
 
     def get_widgets_at(self, x: int, y: int) -> Iterable[tuple[Widget, Region]]:
@@ -531,10 +563,15 @@ class Compositor:
             Iterable[tuple[Widget, Region]]: Sequence of (WIDGET, REGION) tuples.
         """
         contains = Region.contains
-        for widget, cropped_region, region, *_ in self:
-            if contains(cropped_region, x, y) and widget.visible:
+        for widget, region in self.layers_visible.get(y, []):
+            if contains(region, x, y) and widget.visible:
                 yield widget, region
 
+        # contains = Region.contains
+        # for widget, cropped_region, region, *_ in self:
+        #     if contains(cropped_region, x, y) and widget.visible:
+        #         yield widget, region
+
     def get_style_at(self, x: int, y: int) -> Style:
         """Get the Style at the given cell or Style.null()
 
diff --git a/src/textual/widgets/_static.py b/src/textual/widgets/_static.py
index 3e75adad8..01af1d953 100644
--- a/src/textual/widgets/_static.py
+++ b/src/textual/widgets/_static.py
@@ -86,12 +86,13 @@ class Static(Widget):
         """
         return self._renderable
 
-    def update(self, renderable: RenderableType = "") -> None:
+    def update(self, renderable: RenderableType = "", *, layout: bool = False) -> None:
         """Update the widget's content area with new text or Rich renderable.
 
         Args:
             renderable (RenderableType, optional): A new rich renderable. Defaults to empty renderable;
+            layout (bool, optional): Perform a layout. Defaults to True.
         """
         _check_renderable(renderable)
         self.renderable = renderable
-        self.refresh(layout=True)
+        self.refresh(layout=layout)